W± bosons produced in proton-proton collisions can be observed in the ALICE muon spectrometer via their decay into single muons at a transverse momentum, pt ~ Mw/2 40 GeV/c. However the identification of these single muons is complicated by a large amount of muonic background, especially in the low pt region. Therefore, it is necessary to apply precise pt cuts below the region of interest. This can be done by means of the High Level Trigger (HLT). In this paper we present the performance of detecting high pt muons at the HLT level. In order to improve the momentum resolution of the L0 trigger, fast clusterization of the tracking chambers together with L0 trigger matching and fast tracking reconstruction is applied. This will reduce the background in the high pt muon analysis